Approximate Symmetries of the Harry Dym Equation

Table 2

Adjoint representation of approximate symmetry of the perturbed Harry Dym equation.

Ad	𝐯1	𝐯2	𝐯3	𝐯4	𝐯5	𝐯6	𝐯7	𝐯8	𝐯9	𝐯10
𝐯1	𝐯1	𝐯2	𝐯3−𝜇𝐯1	𝐯4	𝐯5−2𝜇𝐯3+𝜇^2𝐯1	𝐯6	𝐯7	𝐯8−𝜇𝐯6	𝐯9	𝐯10−2𝜇𝐯8+𝜇^2𝐯6
𝐯2	𝐯1	𝐯2	𝐯3	𝐯4−12𝜇𝐯2	𝐯5	𝐯6	𝐯7	𝐯8	𝐯9−3𝜇𝐯7	𝐯10
𝐯3	𝑒^𝜇𝐯1	𝐯2	𝐯3	𝐯4	𝑒^−𝜇𝐯5	𝑒^𝜇𝐯6	𝐯7	𝐯8	𝐯9	𝑒^−𝜇𝐯10
𝐯4	𝐯1	𝑒^12𝜇𝐯2	𝐯3	𝐯4	𝐯5	𝐯6	𝑒^3𝜇𝐯7	𝐯8	𝐯9	𝐯10
𝐯5	𝐯1+2𝜇𝐯3+𝜇^2𝐯5	𝐯2	𝐯3+𝜇𝐯5	𝐯4	𝐯5	𝐯6+2𝜇𝐯8+𝜇^2𝐯10	𝐯7	𝐯8+𝜇+𝐯10	𝐯9	𝐯10
𝐯6	𝐯1	𝐯2	𝐯3−𝜇𝐯6	𝐯4	𝐯5−2𝜇𝐯8	𝐯6	𝐯7	𝐯8	𝐯9	𝐯10
𝐯7	𝐯1	𝐯2	𝐯3	𝐯4−3𝜇𝐯7	𝐯5	𝐯6	𝐯7	𝐯8	𝐯9	𝐯10
𝐯8	𝐯1+𝜇𝐯6	𝐯2	𝐯3	𝐯4	𝐯5−𝜇𝐯10	𝐯6	𝐯7	𝐯8	𝐯9	𝐯10
𝐯9	𝐯1	𝐯2+3𝜇𝐯7	𝐯3	𝐯4	𝐯5	𝐯6	𝐯7	𝐯8	𝐯9	𝐯10
𝐯10	𝐯1+2𝜇𝐯8	𝐯2	𝐯3+𝜇𝐯10	𝐯4	𝐯5	𝐯6	𝐯7	𝐯8	𝐯9	𝐯10